F(x)=2/36x-5

Solution for F(x)=2/36x-5 equation:

(F)=2/36F-5

We move all terms to the left:

(F)-(2/36F-5)=0


Domain of the equation: 36F-5)!=0

F∈R


We get rid of parentheses

F-2/36F+5=0

We multiply all the terms by the denominator


F*36F+5*36F-2=0

Wy multiply elements

36F^2+180F-2=0

a = 36; b = 180; c = -2;
Δ = b2-4ac
Δ = 1802-4·36·(-2)
Δ = 32688
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{32688}=\sqrt{144*227}=\sqrt{144}*\sqrt{227}=12\sqrt{227}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(180)-12\sqrt{227}}{2*36}=\frac{-180-12\sqrt{227}}{72}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(180)+12\sqrt{227}}{2*36}=\frac{-180+12\sqrt{227}}{72}
$